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Solve Inequalities

This lesson can be used for revision for the higher Maths GCSE. The examples are quick and concise with exam style questions, go to GCSE Maths if you need more in-depth explanations.

How to draw inequalities on the number line?
How to solve inequalities?

Example 1:
(a) x > -3
Show this inequality on the number line.
(b) Solve the inequality 7y - 34 ≤ 8
(c) Write down the integer values of x that satisfy the inequality -2 ≤ x < 3

Example 2:
(a) On the number line below, show the inequality -2 < y < 3
(b) Here is an inequality, in x, shown on a number line. Write down the inequality.
(c) Solve the inequality 4t - 5 > 11

Example 3:
-3 < n ≤ 1 where n is an integer
(a) Write down all the possible values of n.
(b) Solve the inequality 3p - 7 > 11

Example 4:
(a) (i) Solve the inequality
5x - 7 < 28
(ii) On the number line, represent the solution set to part (i)
(b) n is an integer such that -4 ≤ 2n < 3.
Write down the possible values of n.

Example 5:
(i) Solve the inequality 7x - 3 > 18
(ii) x is a whole number such that 7x - 3 > 18
Write down the smallest value of x.

Example 6:
(a) Solve 5x + 12 < 17
(b) Solve the inequality 3(2y + 1) > 10
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